How to justify the Panel Data Model with lagged independent variables ?

[Muhammad Salahuddin]

Dear scholars,

In my research, I am constructing two-panel models: one-First Differencing Model and secondly -Panel data model with lagged independent variables. The employment and real-wage are used as the dependent variables for the first and second model respectively.

For the first one, I have enough justification and evidence to use the First Difference model, however, for the second model, the same model is not significant. But the Panel data model with lagged independent variables is significant and easy to analyze this model.

In this scenario, how can I justify the panel data model with lagged independent variables?
Or, which test should I do for this?
Or, is it enough to use only the Panel Data Model with lagged independent variables without FE and RE models?

Noted that I have already done Unit Root/Cross Section Dependence/ Cointegration tests. It has a Unit root, CD and cointegration.

Thanks

[Phil Bromiley]

You will increase your chances of useful answer by following the FAQ on asking questions – provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

First differencing is a way to estimate a model, but you don't tell us precisely what model you are estimating.

Many people lag the independent variables and panel data to try to reduce the possibility of reverse causality.

It's not clear what you mean by a panel data model without fixed effects or random effects. Without them, you're doing a pooled OLS probably. There are good reasons why one would want to use the panel estimators – they control for unobserved heterogeneity.